Problem 4: Betty and Bob are short 200 shares of XYZ @48 and long 5 October...

Question

Question

Answer 1

Answer #1

Let X be the stock Price ag expiration.

Value of short position = - 200 x X = - 200X

Value of long call = 5 x max (X - 50, 0)

Hence, formula for W = 5 x max (X - 50, 0) - 200X

P&L, Y = W - Cost = 5 x max (X - 50, 0) - 200X - (3 x 5 - 200 x 48) = 9585 + 5 x max (X - 50, 0) - 200X

The table:

The graph:

12000 10000 8000 6000 4000 2000 10 20 30 40 50 60 70 80 90 -2000 -4000 -6000 -8000

Break even point:

9585 + 5 x max (X - 50, 0) - 200X = 0

For X < 50,

9585 - 200X = 0

Hence, X = 9585 / 200 = 47.925

For X > 50,

9585 + 5 x (X - 50) - 200X = 0

Hence, 195X = 9335

Hence, X = 9335 / 195 = 47.87 but this is not > 50. Hence, this solution is rejected.

Hence, the break even point is X = 47.925

Answer 2

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